Critical Issues and Practices in Gifted Education by Jonathan Plucker

Author:Jonathan Plucker
Language: eng
Format: epub
Publisher: Sourcebooks

Chapter 29

Mathematics Gifted Education

M. Katherine Gavin & Jill L. Adelson

This chapter addresses the major issues facing educators, administrators, and parents in nurturing mathematical talent in students. The focus is on presenting relevant research and guidance on the application of this research so that the reader will be able to make informed decisions that will benefit mathematically gifted students. To varying degrees, the research on this topic addresses the following questions:

• How can we identify students who are mathematically gifted?

• What kinds of programming options for these students have research support?

• What instructional approaches and grouping models work best for these options?

• What research-based curriculum is appropriate for mathematically gifted elementary students?

THE DEFINITION OF MATHEMATICAL GIFTEDNESS

Providing appropriate services for mathematically gifted students is complex, in part because the definition of mathematical giftedness is not universal. How one defines mathematical giftedness, in turn, affects how students are identified for services and the actual services rendered. Often, mathematical giftedness is defined empirically as a score on an ability, aptitude, or achievement test, such as an IQ test, the SAT-M, or the mathematics sections of the Iowa Tests of Basic Skills (ITBS). Although testing provides an easy means for identification, it skirts the issue of what mathematical giftedness is.

The major research-based work focused on defining the characteristics of mathematically talented students was conducted by Krutetskii (1976) through his process of interviews and observations. These characteristics as a definition of mathematical talent have been used by Russian educators for more than 50 years (Sowell, Bergwell, Zeigler, & Cartwright, 1990). Through his research, Krutetskii identified four major components of mathematical giftedness: flexibility, curtailment, logical thought, and formalization. Flexibility is being able to switch strategies in solving a problem easily. Curtailment means being able to skip explicit steps when problem solving as though looking at the solution as a whole instead of as a series of steps. Krutetskii also found that mathematically gifted students follow a logical thought process and look at the world from a logical perspective so that they filter all incoming data through this lens. The fourth component of mathematical giftedness is formalization, the ability to see the overall structure of a problem and to make generalizations from only a few examples.

One reason that the definition of mathematical giftedness is elusive is that there are different types of talent within the domain itself. Mathematically gifted students exhibit a variety of characteristics and not all the same ones. Some students have an “algebraic cast of mind” and tend to be very abstract, while others are more “geometric” and have facility with visualizing problems pictorially. Then there are some who possess a “harmonic” mind with a combination of both algebraic and geometric casts of mind (Krutetskii, 1976). It is important to note that Krutetskii, along with more current researchers, specifically identified swiftness, computational ability, memory for formulas, and other details as “not obligatory” though useful characteristics of mathematical giftedness (Davidson & Sternberg, 1984; Krutetskii, 1976; Sowell et al., 1990). Other characteristics of mathematically gifted students include their focus on conceptual understanding (Sheffield et al.

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